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  2. Trachtenberg system - Wikipedia

    en.wikipedia.org/wiki/Trachtenberg_system

    Take half of the neighbor, then, if the current digit is odd, add 5. Example: 42×5=210 Half of 2's neighbor, the trailing zero, is 0. Half of 4's neighbor is 1. Half of the leading zero's neighbor is 2. 43×5 = 215 Half of 3's neighbor is 0, plus 5 because 3 is odd, is 5. Half of 4's neighbor is 1. Half of the leading zero's neighbor is 2. 93 ...

  3. Multiplication algorithm - Wikipedia

    en.wikipedia.org/wiki/Multiplication_algorithm

    If a positional numeral system is used, a natural way of multiplying numbers is taught in schools as long multiplication, sometimes called grade-school multiplication, sometimes called the Standard Algorithm: multiply the multiplicand by each digit of the multiplier and then add up all the properly shifted results.

  4. Karatsuba algorithm - Wikipedia

    en.wikipedia.org/wiki/Karatsuba_algorithm

    The standard procedure for multiplication of two n-digit numbers requires a number of elementary operations proportional to , or () in big-O notation. Andrey Kolmogorov conjectured that the traditional algorithm was asymptotically optimal, meaning that any algorithm for that task would require () elementary operations.

  5. Schönhage–Strassen algorithm - Wikipedia

    en.wikipedia.org/wiki/Schönhage–Strassen...

    The Schönhage–Strassen algorithm was the asymptotically fastest multiplication method known from 1971 until 2007. It is asymptotically faster than older methods such as Karatsuba and Toom–Cook multiplication, and starts to outperform them in practice for numbers beyond about 10,000 to 100,000 decimal digits. [2]

  6. Surreal number - Wikipedia

    en.wikipedia.org/wiki/Surreal_number

    If a big game decomposes into two smaller games, and the small games have associated Games of x and y, then the big game will have an associated Game of x + y. A game composed of smaller games is called the disjunctive sum of those smaller games, and the theorem states that the method of addition we defined is equivalent to taking the ...

  7. Mental calculation - Wikipedia

    en.wikipedia.org/wiki/Mental_calculation

    If one has a two-digit number, take it and add the two numbers together and put that sum in the middle, and one can get the answer. For example: 24 x 11 = 264 because 2 + 4 = 6 and the 6 is placed in between the 2 and the 4. Second example: 87 x 11 = 957 because 8 + 7 = 15 so the 5 goes in between the 8 and the 7 and the 1 is carried to the 8.